We consider radial solutions to the Cauchy problem for a linear wave equation with a small short-range electromagnetic potential (depending on space and time) and zero initial data. We present two dispersive estimates that provide, in particular, an optimal decay rate in time for the solution. Also, we apply these estimates to obtain similar results for the linear massless Dirac equation perturbed by a potential.
Submitted December 12, 2006. Published October 29, 2008.
Math Subject Classifications: 35A08, 35L05, 35L15, 58J37, 58J45.
Key Words: Wave equation; electromagnetic potential; short-range; Dirac equation; dispersive estimate; decay estimate.
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| Davide Catania |
Dipartimento di Matematica, Facoltà di Ingegneria
Università di Brescia, Via Valotti 9, 25133 Brescia, Italy
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